I don't think that this chip (with erased markings) does anything clever. In fact, it looks pretty much like 74HC244.
Parallel to USB converters do exist, but I don't think they are worth the trouble. You can buy an ISP programmer, which are extremely cheap these days, and wire it directly to the microcontroller pins.
Another alternative would be to use a bit-bang programmer. They are typically based on FTDI FT232RL USB to serial converter. They are quite easy to build and can also be used for UART communications between your PC and the microcontroller.
edit: You can use ProgISP software to see if it works with your board, which supports parallel port programming (if you can find a motherboard with LPT port of course). However you might need to reconfigure the parallel port pins corresponding to the data lines (MISO, MOSI, SCK and RST). If you are lucky, it will work with default settings.
I haven't worked with the classic series of Atmel MCUs, but I believe that any programmer that supports 8051 will work with your chip. Search for '8051 USB programmer' - I'm pretty sure you'll be able to buy one locally.